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Simplify the expression. −8(x−3y)+5(−2x−7y) NOTE: On the sample work, this is a multiple choice question, but on the test, you will be required to show your work for each step to receive credit for this question. Practice writing this out on paper now, so you are prepared to show your work for the test. (1 point) Responses −2x−11y negative 2 x minus 11 y 2x+11y 2 x plus 11 y 18x+59y 18 x plus 59 y −18x−11y

1 answer

Let's simplify the given expression step by step:

The expression is: \[ -8(x - 3y) + 5(-2x - 7y) \]

Step 1: Distribute the terms

First, we distribute \(-8\) across \((x - 3y)\) and \(5\) across \((-2x - 7y)\).

  1. Distributing \(-8\): \[ -8(x) + (-8)(-3y) = -8x + 24y \]

  2. Distributing \(5\): \[ 5(-2x) + 5(-7y) = -10x - 35y \]

Step 2: Combine the results

Now, we can combine the results from step 1: \[ -8x + 24y - 10x - 35y \]

Step 3: Combine like terms

Now we will combine the like terms of \(x\) and \(y\):

  • For \(x\): \[ -8x - 10x = -18x \]

  • For \(y\): \[ 24y - 35y = -11y \]

Final Expression

Putting it all together, we simplify it to: \[ -18x - 11y \]

Conclusion

Thus, the simplified expression is: \[ -18x - 11y \]

So the correct choice from the given multiple choices is −18x−11y.